Three men and their wives sit randomly on 6 seats in 2 rows (each row has 3 seats).
- What’s the number of different ways they can sit?
- What is the probability that all the men sit in one row?
- What is the probability that every man sits facing his wife?
- What is the probability that only one man sits facing his wife? (I believe "at least one man" would do. Else it would be too complicated?)
I attempted solving the questions. The first one is surely right, but for the next two after too many tries, I solved them programmatically, that is – recursively listing all permutations and filtering the ones that fulfill the required condition.
My solution:
- (6P6)=720
- 72/720 = 1/10
- 48/720 = 1/15
- Couldn't solve it.
Can anyone assist on how to solve them mathematically? There should be an easy way that I'm missing out, the way I solved them probably gets me the right answer but it's not logical for a human to do.
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